The 30-year fixed rate mortgage averaged 3.34 percent for the week ending January 3, which was just a 0.01 percent decrease from the previous week. The 15-year fixed-rate mortgage also averaged 2.64 percent in the same week.

"Mortgage rates started the year near record lows, which should continue to aid the ongoing housing recovery," said Frank Nothaft, vice president and chief economist of Freddie Mac. "New home sales rose in November to a two-year high and were up 15.3 percent from the previous November. Similarly, pending sales on existing homes increased for the third month in November to the strongest pace since April 2010."

There have also been reports of 55,000 completed foreclosures in November, which could encourage more first-time homebuyers to take advantage of the low prices being offered around the country.